Step 1 :
Divide $ 15890 $ by $ 10890 $ and get the remainder

$$ 15890 : 10890 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

The remainder is positive ($ 5000 > 0 $), so we will continue with division.

Step 2 :
Divide $ 10890 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 10890 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 890 } \text{ ) } $$

The remainder is still positive ($ 890 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 890 } $ and get the remainder

$$ 5000 : 890 = 5 \text{ ( remainder is } \color{blue}{ 550 } \text{ ) } $$

The remainder is still positive ($ 550 > 0 $), so we will continue with division.

Step 4 :
Divide $ 890 $ by $ \color{blue}{ 550 } $ and get the remainder

$$ 890 : 550 = 1 \text{ ( remainder is } \color{blue}{ 340 } \text{ ) } $$

The remainder is still positive ($ 340 > 0 $), so we will continue with division.

Step 5 :
Divide $ 550 $ by $ \color{blue}{ 340 } $ and get the remainder

$$ 550 : 340 = 1 \text{ ( remainder is } \color{blue}{ 210 } \text{ ) } $$

The remainder is still positive ($ 210 > 0 $), so we will continue with division.

Step 6 :
Divide $ 340 $ by $ \color{blue}{ 210 } $ and get the remainder

$$ 340 : 210 = 1 \text{ ( remainder is } \color{blue}{ 130 } \text{ ) } $$

The remainder is still positive ($ 130 > 0 $), so we will continue with division.

Step 7 :
Divide $ 210 $ by $ \color{blue}{ 130 } $ and get the remainder

$$ 210 : 130 = 1 \text{ ( remainder is } \color{blue}{ 80 } \text{ ) } $$

The remainder is still positive ($ 80 > 0 $), so we will continue with division.

Step 8 :
Divide $ 130 $ by $ \color{blue}{ 80 } $ and get the remainder

$$ 130 : 80 = 1 \text{ ( remainder is } \color{blue}{ 50 } \text{ ) } $$

The remainder is still positive ($ 50 > 0 $), so we will continue with division.

Step 9 :
Divide $ 80 $ by $ \color{blue}{ 50 } $ and get the remainder

$$ 80 : 50 = 1 \text{ ( remainder is } \color{blue}{ 30 } \text{ ) } $$

The remainder is still positive ($ 30 > 0 $), so we will continue with division.

Step 10 :
Divide $ 50 $ by $ \color{blue}{ 30 } $ and get the remainder

$$ 50 : 30 = 1 \text{ ( remainder is } \color{blue}{ 20 } \text{ ) } $$

The remainder is still positive ($ 20 > 0 $), so we will continue with division.

Step 11 :
Divide $ 30 $ by $ \color{blue}{ 20 } $ and get the remainder

$$ 30 : 20 = 1 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

The remainder is still positive ($ 10 > 0 $), so we will continue with division.

Step 12 :
Divide $ 20 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 20 : \color{blue}{ \boxed { 10 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 10 }} $.

This solution can be visualized using a Venn diagram.

The GCD equals the product of the numbers at the intersection.

GCD Calculator